Strange results from Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg16022] Strange results from Integrate
- From: Sergio Terrazas <sterraza at campus.cdj.itesm.mx>
- Date: Sat, 20 Feb 1999 02:52:08 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Dear mathgroupers:
I was working with a probability density function when I got the following
strange result:
f[x_]= Exp[-20 (x-12.5)]
Integrate[f[x],{x,12.6,Infinity}]
Out= 6.51852 x 10^92 =A1=A1What?!!
NIntegrate[f[x],{x,12.6,Infinity}]
Out= 0.135335 (Correct!)
If I use exact numbers like 125/10 instead of 12.5, I get
f[x_]= Exp[-20 (x-12.5)] (Note the 12.5)
Integrate[f[x],{x,126/10,Infinity}] (Note the 126/10)
Out= 0 ( ???)
Now with both exact values:
f[x_]= Exp[-20 (x-125/10)] (Note the 125/10)
Integrate[f[x],{x,126/10,Infinity}] (Note the 126/10)
Out= 1/E^2 (Correct!)
Now using the fundamental theorem of calculus:
(Using the definition of f with reals)
f[x_]= Exp[-20 (x-12.5)]
g[x_]=Integrate[f[x],x]
Out= -E^(250-20x) (Correct)
g[Infinity]-g[12.6] = 0.135335
What is going on?
Is Integrate just unrelaiable with non exact numbers?? (Scary !!)
I will appreciate any comments from the insiders.
Thanks in advance ( Oh! by the way, I an using v. 3.0.1 for windows)
Sergio Terrazas
Juarez, Mexico